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PoS - Proceedings of Science
Volume 310 - XVII International Conference on Hadron Spectroscopy and Structure (Hadron2017) - Posters
On the coherent inelastic binary and multiparticle processes in ultrarelativistic hadron-nucleus, photon-nucleus and nucleus-nucleus collisions
V.V. Lyuboshitz* and V.L. Lyuboshitz
Full text: pdf
Pre-published on: February 20, 2018
Published on: March 20, 2018
Abstract

The coherent inelastic processes of the type ab,
which may take place in the interaction of hadrons and γ quanta with
nuclei at very high energies ( the nucleus remains the same ), are
theoretically investigated. For taking into account the influence of
matter inside the nucleus, the optical model based on the concept of
refraction index is applied .
Analytical formulas for the effective
cross section σcoh(ab) are obtained,
taking into account that at ultrarelativistic energies the
main contribution into
σcoh(ab)
is provided by very small transferred momenta in the vicinity of the
minimum longitudinal momentum transferred to the nucleus. It is shown
that the cross section σcoh(ab) may be
expressed through the "forward" amplitudes of inelastic scattering
fa+Nb+N(0) and elastic scattering
fa+Na+N(0), fb+Nb+N(0)
on a separate nucleon, and it depends on the ratios La/R and
Lb/R, where La,
Lb are the respective mean free paths in the nucleus matter for the
particles a, b and R is the nuclear radius.

In doing so,
several characteristic cases with different relations of the magnitudes
La,Lb,R are considered in detail. When
La/R1, but Lb/R1 ( or, on the contrary,
La/R1 but Lb/R1 ), then
the cross section σcoh(ab) is equal to
the ratio of the "forward" cross sections of inelastic scattering
a+Nb+N and elastic
scattering of the particle b (or, respectively, a) on a nucleon,
multiplied by
the cross section of scattering on the "black" nucleus πR2.
The cases La/R1, Lb/R and
L_a/R \gg 1, L_b/R \ll 1 (for heavy nuclei) correspond,
in particular,
to the coherent production of vector mesons
\rho^0, \omega, \phi at the interaction of very
high energy photons with nuclei, and some numerical estimates are
made for the coherent process \gamma \rightarrow \rho^0 on
the Pb nucleus.
Meantime, when both the conditions L_a/R \gg 1 and L_b/R\gg 1 are
satisfied,
then \sigma_{{\rm coh}} (a \rightarrow b ) is proportional to the factor
R^4/k^2, where k is the initial energy of the particle a
in the laboratory frame.

The formalism described above is generalized also for the case of coherent
inelastic multiparticle processes on a nucleus of the type
a \rightarrow \{ \,b_1, b_2, b_3 ....b_i \,\} and for the case
of coherent processes in collisions of two ultrarelativistic nuclei.

DOI: https://doi.org/10.22323/1.310.0227
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